Module d'un nombre complexe - Corrigé

Énoncé

Calculer le module des complexes suivants.

• `z_1=-1+3i`  
  
• `z_2=5` ; `z_3=-6`   
  
• `z_4=2+3i`  
• `z_5=-2i`  
• `z_6=\frac{2}{5}i`

Solution

• \(\left\vert z_1 \right\vert =\left\vert -1+3i \right\vert =\sqrt{(-1)^2+3^2} =\sqrt{1+9} =\sqrt{10}\)
  
• \(\left\vert z_2 \right\vert =\left\vert 5 \right\vert =\sqrt{5^2} =\sqrt{25} =5\)
• \(\left\vert z_3 \right\vert =\left\vert -6 \right\vert =\sqrt{(-6)^2} =\sqrt{36} =6\)
• \(\left\vert z_4 \right\vert =\left\vert 2+3i \right\vert =\sqrt{2^2+3^2} =\sqrt{4+9} =\sqrt{13}\)
  
• \(\left\vert z_5 \right\vert =\left\vert -2i \right\vert =\sqrt{(-2)^2} =\sqrt{4} =2\)
  
• \(\left\vert z_6 \right\vert =\left\vert \dfrac{2}{5}i \right\vert =\sqrt{\left(\dfrac{2}{5}\right)^2} =\sqrt{\dfrac{4}{25}} =\dfrac{2}{5}\)